Asymptotic behavior of solutions for a class of difference equations

[摘要] Consider the difference equation (1) x(n) - x(n-1) = -F(x(n)) + G(x(n-k)), where k is a positive integer, F and G are continuous, and F is increasing on R. We show that when Fly) greater than or equal to G(y) for y is an element of R, every solution of (1) tends to either a constant or -infinity as n --> infinity; while when F(y) less than or equal to G(y) for y is an element of R, every solution of (1) tends to either a constant or infinity as n --> infinity. In particular, if F(y) = G(y) for y is an element of R, then every solution of (1) tends to a constant as n --> infinity. (C) 1996 Academic Press, Inc.

[发布日期] 1996-12-15